Which function will produce the same graph as the function shown below?
v=(r+1) (r+3)
OAVt3 =x(r- 1)
O B.-3 = (r- )²
Oc.v=xt4r- 3
OD.V=r+4r+3

9514 1404 393

Answer:

  B)  12

Step-by-step explanation:

The base is twice the length of the midline.

  QS = 2·YZ

  3x -8 = 2(x +2) . . . . . . . substitute given values

  3x -8 = 2x +4 . . . . . . eliminate parentheses

  x = 12 . . . . . . . . . . . add 8-2x

The graph that shows a proportional relationship between x and y is given as follows:

Graph D.

A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.

The equation that defines the proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

From the equation y = kx we have that it is a linear function with intercept of zero, meaning that the graph D represents the proportional relationship for this problem.

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Answer:

Step-by-step explanation:

Volume = 1/3 * B * h

B = 8 * 8 = 64

h = 15.5

Volume = 1/3 * 64 * 15.5

Volume = 2976 cu in

Answer: The simple interest rate is 3%.

Step 1: Calculate the principal (P)

P = $750

Step 2: Calculate the interest (I)

I = $228.00

Step 3: Calculate the time (t)

t = 7.6 years

Step 4: Calculate the simple interest rate (r)

r = I / Pt

r = $228.00 / ($750 x 7.6)

r = 0.03 or 3%

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Answer:

-11

Step-by-step explanation:

Notice how

\(f(x)=x^{2} +8x+1\)

So when we have

\(f(-6)=(-6)^{2} +8(-6)+1= 36-48+1=-11\)

The answer is:

f(-6) = -11

Step-by-step explanation:

Plug in -6 for x:

\(\sf{f(x)=x^2+8x+1}\)

\(\sf{f(-6)=(-6)^2+8(-6)+1}\)

Simplify this:

\(\sf{f(-6)=36-48+1}\)

\(\sf{f(-6)=-12+1}\)

\(\sf{f(-6)=-11}\)

Answer:

the answer is D. F(x) = 1/x(x-3)

Step-by-step explanation:

Answer:

The slope of the parallel line to the line 2x + 5y = -10 is \(-\frac{2}{5}\)

Step-by-step explanation:

Parallel lines have equal slopes and different y-intercepts

To find the slope of the line from the equation of the line, then put the equation in the form y = m x + b, where

Let us solve the question

∵ The equation of a line is 2x + 5y = -10

→ Put the equation in the form above

→ Subtract x from both sides to move 2x from the left side to the

   right side

∴ 2x - 2x + 5y = -10 - 2x

∴ 5y = -10x - 2x

→ Make the coefficient of y equal 1 by dividing all terms by 5

∵ \(\frac{5y}{5}=-\frac{10}{5}-\frac{2x}{5}\)

∴ y = -2 - \(\frac{2}{5}x\)

→ Compare it by the form of the equation above

∴ m = \(-\frac{2}{5}\)

∴ The slope of the given line is \(-\frac{2}{5}\)

→ We need the slope of the line which is parallel to the given line

∵ Parallel lines have the same slopes

∴ The slope of the parallel line to the line 2x + 5y = -10 is \(-\frac{2}{5}\)

Answer:

A = $32

B = $18

Step-by-step explanation:

50 - 14 = 36

36 ÷ 2 = 18

18 + 14 = 32

18 + 32 = 50

The cost for video game A is $32

The cost for video game B is $18

Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.

Given:

price for video game A is $14 more than the price for video game B.

let the price of video game B is x

Then price for video game A = x+14

Total cost of both game = 50

x+x+14= 50

2x= 36

x=18

Hence,  cost for video game A is $32 and  cost for video game B is $ 18

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Answer:

-5/4

Step-by-step explanation:

Let \((x_1,y_1)=(-4,4)\) and \((x_2,y_2)=(0,-1)\). The slope of the line would be:

\(\displaystyle \frac{y_2-y_1}{x_2-x_1}=\frac{-1-4}{0-(-4)}=\frac{-5}{4}=-\frac{5}{4}\)

Answer: -5/4

Step-by-step explanation:

To find the slope between two points, you can use the formula:

Slope = (y2 - y1)/(x2 - x1)

Using the points (0, -1) and (-4, 4), we can substitute the coordinates into the formula:

slope = (4 - (-1))/(-4 - 0)

slope = (4 + 1)/(-4)

slope = 5/-4

Therefore, the slope between the two points is -5/4.

The domain is {-8, -12, 1, -2} and the range is {5, -11, -1, -4}

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have

(-8,5) (-12,-11)  (1-1) (-2,-4)

The domian is the set of the input values

Using the ordered pairs as a guide, we have

Domain = {-8, -12, 1, -2}

For the range, we have

The range is the set of the output values

So, we have

Range = {5, -11, -1, -4}

Hence, the range is  {5, -11, -1, -4}

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Answer:

10.2% chance

Step-by-step explanation:

There are 12 peaches and 8 bananas for a total of 20 pieces of fruit.

So we can write it:

\(\frac{12}{20} * \frac{11}{19} * \frac{10}{18} * \frac{9}{17}\) =  \(\frac{11880}{116,280}\) = .102 or 10.2% chance

For ease multiply all numerators (top numbers) together, then multiply the denominators (bottom numbers) together, and then divide.

12 * 11 * 10 * 9 = 11880

20 * 19 * 18 * 17 = 116,280

We start with 12 peaches and 20 total fruit, as we select a peach the number of peaches and total fruit goes down by one. We do this 4 times because you draw 4 fruits. If you select 1 fruit your chances of it being a peach are 12/20, each time you select a fruit the chances of it being a peach go down because you have 1 less total fruit, and 1 less peach. This is why you multiply each probability together.

Answer:

10.2% probability

Step-by-step explanation:

12 peaches

8 bananas

Chance of getting a peach the first time is 12/20 the second time is 11/19, third 10/18, and fourth 9/17

11880/116280 = .1022 = 10.2% probability

Answer:

x = 9

Step-by-step explanation:

To solve the equation 2x - 7 + 3x = 4x + 2 for x, you can follow these steps:

Combine like terms on both sides of the equation. Add the x terms together and move the constant terms to one side of the equation:

2x + 3x - 4x = 2 + 7

Simplifying the left side: x = 9

Simplify the right side of the equation:

x = 9

Therefore, the solution to the equation is x = 9.

Answer:

Explanation:

From the information,

equation of curve = y^2 = 2x^3

equation of line = 4x - 3y + 1 = 0

The first step is to find the slope of the line. Recall, the equation of a line in the slope intercept form is expressed a

y = mx + c

where

m represents slope

We would rearrange the given equation. We have

3y = 4x + 1

y = 4x/3 + 1/3

Thus,

m = 4/3

The slope of the perpendicular line = - 1/m = - 3/4

For the curve, we would find the derivative.

y = (2x^3)^1/2

y' = 2^3/2 * x^3/2

f'(x) = (3√x)/√2

We would equate the derivative to the slope of the perpendicular line. We have

(3√x)/√2 = - 3/4

3√x * 4 = - 3√2

12√x = - 3√2

√x = - 3√2/12

√x = -√2/4

Square both sides

x = (-√2/4)^2 = 2/16

x =

Substituting x = 1/8 into y = (2x^3)^1/2, we have

y = (2(1/8)^3)^1/2

y = √256

y =

Answer:

Step-by-step explanation:

A. when you multiply exponents with a common base you keep the base and add the exponents. In this case you would keep the 6 and add the -5 and 2 so the answer would be:

6^-3 which is not equivalent

B. You can distribute the exponent in to the parenthesis.

(1^5)/(6^2)^5

when you have an exponent to an exponent you mutliply. so the answer would be:

1^5/6^10

1^5 is always going to be 1 so you actually have:

1/6^10

when the exponent is on the bottom you can bring it to the top by making it negative, so the final answer for B is:

6^-10 which is equivalent

C. Same rules as B, multiply an exponent to an exponent.

6^(-5*2) = 6^-10 which is equivalent

D. When you are dividing exponents with a common base you subtract the top and bottom exponents. So in this case you have:

6^(-3-7) = 6^-10 which is equivalent

E. Using the rules from eariler the numerator can be simplified by adding the exponents.

6^5 * 6^-3 = 6^(5-3) = 6^2

which leaves you with:

6^2/6^-8

From there you can either bring the 6^-8 to the numberator to make it positive which simplifies to:

6^2 * 6^8 = 6^(2+8) = 6^10 which is not equivalent

or you can subtract the top and bottom exponents:

6^2/6^-8 = 6^(2-(-8))

the double negative cancels to a positive and you getL

6^(2+8) = 6^10 which is not equivalent

so B, C, and D are equal to 6^-10

Answer:

The solution to the system is:

x = -63

y = 10

Explanation:

Given the pair of equations:

x + 3y = -33 ......................................................(1)

-4x + 5y = -38 ...................................................(2)

Multiply (1) by 4

4x + 12y = -132 ..................................................(3)

Add (2) and (3)

-4x + 4x + 5y + 12y = -38 - 132

17y = 170

Divide both sides by 17

y = 170/17 = 10

Substitute y by 10 in (1)

x + 3(10) = -33

x + 30 = -33

Subtract 30 from both sides

x = -33 - 30

x = -63

Therefore,

x= -63, y = 10

The area of the square is given as 100 square unit

You should be aware that the square has all its sides equal

The perpendicular from opposite vertices represent distance

The given vertices are

(2,2) and (10,8)

Using the formula for distance between two points

d=√(10-2)²+(8-2)²

d=√8²+6²

d = √64+36

d=√100

This implies that d=10

The area of a square is given as s²

Area = 10²

Atrea = 100 square units

In conclusion, the area of the square is 100 square units

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Translated question:

The vertices of a square ABCD are A(2,2) and B(10,8), Find the area of the square

Answer: There will be approximately 1154.6 people attending.

Step-by-step explanation:

To find out how many people will be attending in 4 years, we can use the formula:

Attendance(future) = Attendance(current) * (1 - rate)^time

Where:

Attendance(current) = 1200 people

Rate = 0.5% (as a decimal = 0.005)

Time = 4 years

So, Attendance(future) = 1200 * (1 - 0.005)^4

Attendance(future) = 1200 * 0.99^4 = 1200 * 0.9605 = 1154.6 people

So, in 4 years, there will be approximately 1154.6 people attending.

Answer:

20:9

Step-by-step explanation:

Here we will simplify the ratio to 40:18 for you and show you how we did it.

To simplify the ratio 40:18, we find the greatest common divisor of 40 and 18, and then we divide 40 and 18 by the greatest common divisor.

The greatest common divisor that you can use to simplify 40:18 is 2. This means the answer to ratio 40:18 simplified is:

20:9

Answer:

I am pretty sure it is a 50% chance.

Step-by-step explanation:

20 + 30 = 50%

We will get y = -7x + 6  in graph y-intercept 6 and slope-7.

The equation of the line with a y-intercept of 6 and a slope of -7 can be written in slope-intercept form as:

y = mx + b

where m is the slope and b is the y-intercept.

Substituting the given values, we get:

y = -7x + 6

So the equation of the line is y = -7x + 6.

slope -7 and y - intercept 6.

Slope intercept form: y = mx + b, m=slope, b = y-intercept

y = -7x + 6

Just plug in a value for x and solve for y

x     y=-7x+6

------------------

0           6

1          -1

If you plot these two points and draw a straight line through them,

that is the graph of the line.

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The mean value is 7.6. Option (D) is the correct answer.

The number of successes in a sample of size n drawn with replacement from a population of size N is frequently modeled using the binomial distribution.

The mean value of a binomial distribution is,

\(\mu =np\\=38*0.2\\=7.6\)

Multiplication:

In mathematics, multiplying two or more numbers yields the product of the numbers. It is one of the basic mathematical operations that we carry out on a regular basis. The most obvious application is using multiplication tables. The multiplication of two numbers in mathematics represents the repeated addition of one number in respect to another. These numbers can be natural numbers, whole numbers, fractions, integers, or other types of numbers. When m is multiplied by n, m is either multiplied by n times or added to itself n times.

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Apologies, but your questions seem to have errors and incomplete information.

For the first question about Jessica and Melissa sharing 12 pieces of dried pears, it is unclear how much Jessica ate as the fraction is missing. Similarly, information about how many pears Melissa ate is also missing. To answer the question accurately, I need the missing information.

For the second question about the children playing in the park, you mentioned that one-third of the children returned home, but you didn't provide the total number of children initially in the park. Without that information, I cannot determine how many children stayed in the park.

Please provide complete and accurate information for a precise answer.

Step-by-step explanation:

right option

...............

The width of the rectangle for which the perimeter is less than 82 feet is 9ft

2(Iength + width) < perimeter

2(32 + x) < 82

64 + 2x < 82

2x < 82 - 64

2x < 18

x < 18/2

x < 9 feet

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The statements supported by the data in the table are:

The mean number of cars sold in a month is the same at both dealerships.

The total number of cars sold is the same at both dealerships.

The data for Admiral Autos shows greater variability.

To determine which statements are supported by the data in the table, let's analyze the given information:

The mean number of cars sold in a month is the same at both dealerships.

To calculate the mean, we need to find the average number of cars sold each month at each dealership.

For Admiral Autos:

(4 + 19 + 15 + 10 + 17) / 5 = 65 / 5 = 13

For Countywide Cars:

(9 + 17 + 14 + 10 + 15) / 5 = 65 / 5 = 13

Since both dealerships have an average of 13 cars sold per month, the statement is supported.

The median number of cars sold in a month is the same at both dealerships.

To find the median, we arrange the numbers in ascending order and select the middle value.

For Admiral Autos: 4, 10, 15, 17, 19

Median = 15

For Countywide Cars: 9, 10, 14, 15, 17

Median = 14

Since the medians are different (15 for Admiral Autos and 14 for Countywide Cars), the statement is not supported.

The total number of cars sold is the same at both dealerships.

To find the total number of cars sold, we sum up the values for each dealership.

For Admiral Autos: 4 + 19 + 15 + 10 + 17 = 65

For Countywide Cars: 9 + 17 + 14 + 10 + 15 = 65

Since both dealerships sold a total of 65 cars, the statement is supported.

The range of the number of cars sold is the same for both dealerships.

The range is determined by subtracting the lowest value from the highest value.

For Admiral Autos: 19 - 4 = 15

For Countywide Cars: 17 - 9 = 8

Since the ranges are different (15 for Admiral Autos and 8 for Countywide Cars), the statement is not supported.

The data for Admiral Autos shows greater variability.

To determine the variability, we can look at the range or consider the differences between each data point and the mean.

As we saw earlier, the range for Admiral Autos is 15, while for Countywide Cars, it is 8. Additionally, the data points for Admiral Autos are more spread out, with larger differences from the mean compared to Countywide Cars. Therefore, the statement is supported.

Based on the analysis, the statements supported by the data are:

The mean number of cars sold in a month is the same at both dealerships.

The total number of cars sold is the same at both dealerships.

The data for Admiral Autos shows greater variability.

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Answer: A)

Step-by-step explanation: khan academy

Answer:

x= 79 y= 15 m=54

Step-by-step explanation:

both triangles are basically mirrored, so since x+11 is in the same position as angle H the real equation would be: x+11=90 and the same thing for y+7 because that side is the same as side FG the equation would be y+7=22. For M since angles E and H are 35 and 90 you just add them together and then subtract them from 180 because are triangles add up to 180 degrees in terms of angles not sides.

Answer:

y = 15

x = 1.93  wrong x = 79

m∠GFH = 54°

Step-by-step explanation:

y + 7 = 22

y = 15

sin 36° = (x + 11)/22

0.5878 = (x + 11)/22

x + 11 = 12.93

x = 1.93

m∠GFH = 90° - 36° = 54°

Answer:

height = 21 cm

Step-by-step explanation:

\(\textsf{Volume of a cone}=\sf \dfrac{1}{3} \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}\)

Given:

Substituting given values into the formula and solving for r:

\(\implies \sf 343 \pi=\dfrac{1}{3} \pi r^2(3r)\)

\(\implies \sf 343=\dfrac{1}{3}\cdot3r^3\)

\(\implies \sf 343=r^3\)

\(\implies \sf r=\sqrt[3]{343}\)

\(\implies \sf r=7\:cm\)

As h = 3r, substitute found value of r into the equation and solve for h:

\(\implies \sf h = 3r\)

\(\implies \sf h=3(7)\)

\(\implies \sf h=21\:cm\)